The purpose of this paper is to prove some theorems which generalize a theorem of M. Tel ci, K. Tas and B. Fisher on compatible mappings and compatible mappings of type (A). Let S, T be two self-mappings of a metric space (X; d). Sessa 7] deenes S and T to be weakly commuting if d(STx; TSx) 6 d(Tx; Sx) for all x in X. Jungck 3] deenes T and S to be compatible ii lim n d(STx n ; TSx n) = 0 whene...

Introduction Sessa [9] generalized the notion of commuting maps given by Jungck [2] and introduced weakly commuting mappings. Further, Jungck [3] introduced more generalized commutativity called compatibility. In 1998, Jungck and Rhoades [4] introduced the notion of weakly compatible maps and showed that compatible maps are weakly compatible but converse need not true. Menger [5] introduced the...

In this paper, we establish a coincidence and a common fixed point for a pair of weakly compatible mappings under (ψ, φ)weakly contractive condition in G-metric spaces. Our results improve and generalize the results of Khandaqji et al. [20]. We also provide an example to support our results. Moreover, we prove that these mappings satisfy Property Q.

The aim of this paper is to prove a common fixed point theorem for two pairs of self mappings in a cone metric space without assuming the normality of cone. Here we consider one pair of compatible mappings of type (R) and another pair of weakly compatible. Our results extend and modify the result of [11] and generalise many other results in the literature. −−−−−−−−−−−−−−−−−−−−−−−−−−−−

In this paper, first we prove fixed point theorems for different variant of compatible maps, satisfying a contractive condition of integral type in fuzzy metric spaces, which improve the results of Branciari [2], Rhoades [33], Kumar et al. [23], Subramanyam [35] and results of various authors cited in the literature of ”Fixed Point Theory and Applications”. Secondly, we introduce the notion of ...

In this paper, first we prove a common fixed point theorem for a pair of weakly compatible self maps in complex valued metric space for rational inequality. Secondly, we prove common fixed point theorems for weakly compatible mappings along with (CLRg) and E.A. properties.

Banach contraction principle is a fundamental result in fixed point theory and has been applied and extended in many different directions. In 2002, Branciari [3] obtained a fixed point theorem for a single mapping satisfying an analogue of Banach’s contraction principle for an integral type inequality. Aliouche [2] established a common fixed point theorem for weakly compatible mappings in symme...